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首页> 外文期刊>Journal of Sound and Vibration >SIMPLIFIED EQUATIONS OF MOTION FOR THE RADIAL-AXIAL VIBRATIONS OF FLUID FILLED PIPES
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SIMPLIFIED EQUATIONS OF MOTION FOR THE RADIAL-AXIAL VIBRATIONS OF FLUID FILLED PIPES

机译：流体填充管径向-轴向振动的简化运动方程

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摘要

The equations of motion for straight fluid filled pipes are greatly simplified. It is found, for frequencies below a third of the ring frequency, that the radial-axial waves in cylinders are as if the circumferential motion were inextensional. This is the fundamental assumption for the analysis. The derivation is also based on the assumption of long axial wavelengths, resulting in the axial inertia of the fluid and the axial flexural stiffness of the pipe wall being negligible. The formulation is restricted to frequencies well below the cut-on of higher order fluid modes. For such frequencies, the compressibility of the fluid is neglected and the internal fluid loading, on the pipe, is approximated as an increase in the radial inertia. Upon this basis, the equations of motion, for each circumferential mode, are similar to those for a Timoshenko beam on a Winkler foundation. Numerical experiments are made, comparing the approximate theory with results from calculations from the Helmholtz equation for the fluid and accurate thin-walled cylinder theory. Criteria for the application of the simplified theory are formulated. (C) 1997 Academic Press Limited. [References: 22]
机译：直线流体填充管的运动方程式大大简化了。已经发现，对于低于振铃频率三分之一的频率，圆柱体中的径向轴向波好像圆周运动是没有延伸的。这是分析的基本假设。该推导也基于长轴向波长的假设，从而导致流体的轴向惯性和管壁的轴向抗弯刚度可以忽略不计。该公式仅限于远低于高阶流体模式的截止频率的频率。对于这样的频率，流体的可压缩性被忽略，并且管道上的内部流体负载被近似为径向惯性的增加。在此基础上，每种圆周模式的运动方程都类似于Winkler基础上的Timoshenko梁的方程。进行了数值实验，将近似理论与Helmholtz方程对流体的计算结果和精确的薄壁圆柱体理论进行了比较。制定了应用简化理论的标准。 （C）1997 Academic Press Limited。 [参考：22]

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